This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std ;
#define mid (l+r)/2
#define pb push_back
#define C continue 
#define lb lower_bound
typedef long long ll ;
typedef vector < int > vi ;
#include "rect.h"
int n , m ;
int a   [2509][2509] ;
int pre [2509][2509] ;
int Sum ( int i , int j , int k , int l ) {
        int sum = 0 ;
        sum += pre [j][l] ;
        sum -= ( i ? pre [i-1][l] : 0 ) ;
        sum -= ( k ? pre [j][k-1] : 0 ) ;
        sum += ( i && k ? pre [i-1][k-1] : 0 ) ;
        return sum ;
}
long long count_rectangles ( vector <vi> A ) {
        n = A .size () ;
        m = A [0] .size () ;
        for ( int i = 0 ; i < n ; i ++ ) {
                for ( int j = 0 ; j < m ; j ++ ) {
                        a [i][j] = A [i][j] ;
                }
        }
        for ( int i = 0 ; i < n ; i ++ ) {
                for ( int j = 0 ; j < m ; j ++ ) {
                        pre [i][j] = a [i][j] ;
                        pre [i][j] += ( i ? pre [i-1][j] : 0 ) ;
                        pre [i][j] += ( j ? pre [i][j-1] : 0 ) ;
                        pre [i][j] -= ( i && j ? pre [i-1][j-1] : 0 ) ;
                }
        }
        ll ans = 0 ;
        for ( int i = 1 ; i < n - 1 ; i ++ ) {
                for ( int k = 1 ; k < m - 1 ; k ++ ) {
                        if ( a [i][k] == 1 ) C ;
                        int l = i , r = n - 1 ;
                        while ( r - l > 1 ) {
                                if ( Sum ( i , mid , k , k ) == 0 ) l = mid ;
                                else r = mid ;
                        }
                        int j = l ;
                        l = k , r = m - 1 ;
                        while ( r - l > 1 ) {
                                if ( Sum ( i , i , k , mid ) == 0 ) l = mid ;
                                else r = mid ;
                        }
                        if ( Sum ( i , j , k , l ) ) C ;
                        if ( Sum ( i , j , k - 1 , k - 1 ) != j - i + 1 ) C ;
                        if ( Sum ( i , j , l + 1 , l + 1 ) != j - i + 1 ) C ;
                        if ( Sum ( i - 1 , i - 1 , k , l ) != l - k + 1 ) C ;
                        if ( Sum ( j + 1 , j + 1 , k , l ) != l - k + 1 ) C ;
                        ans ++ ;
                }
        }
        return ans ;
}
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